Vibratory sensor operating as a rate gyro about two axes and as a rate integrating gyro about the third one

ABSTRACT

A vibrating structure gyroscope comprises a resonant body, a drive transducer for driving resonant motion of the body, a pick-off for producing signals representative of the resonant motion, and a signal processor for extracting z-axis orientation information and x- and y-axis rate information from the signals. The resonant body is planar and the resonant motion takes place in a vibration mode pattern whose orientation angle with respect to the body varies in accordance with z-axis orientation of the body and couples energy into an out-of-plane response mode motion in accordance with rotation of the body about the x- or y-axis. The signal processor resolves the out-of-plane response mode motion with reference to a z-axis orientation signal to extract the x- and y-axis rate information.

This application is the US national phase of international applicationPCT/GB01/00057 filed 08 JAN. 2001, which designates the US.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to multi-axis sensing devices and moreparticularly to vibrating structure gyroscopes that employ a resonantelement.

2. Discussion of Prior Art

Vibrating structure gyroscopes have been fabricated using a variety ofstructures for the resonant element including beams tuning forks,cylinders and rings. Aside from measurement of the rate of rotationabout a particular axis, these devices are also capable of operation in“whole angle” or “gyroscope” mode in which the device output gives adirect measure of the angle of rotation about a particular axis, asdescribed in U.S. Pat. No. 5,218,867. This mode of operation is known togive advantages in terms of improved scalefactor performance,particularly in applications where the device is subjected to sustainedhigh rates of rotation.

Planar rings have been shown to be particularly versatile, withsingle-axis rate zero variants being commercially available using bothconventionally fabricated and micro-machined resonators.

Conventional single-axis planar ring gyroscopes typically use cos 2θin-plane vibration mode pairs. For a perfectly symmetric resonator therewill be two degenerate modes at a mutual angle of 45°. These are shownschematically in FIG. 1a (cos 2θ mode) and FIG. 1b (sin 2θ mode) whichshow the ring distortion at the two extremes of motion during a singlevibration cycle. One of these modes is excited as the carrier mode (FIG.1a). When the structure is rotated about the axis normal to the plane ofthe ring (the z-axis). Coriolis forces couple energy into the responsemode (FIG. 1b). The Coriolis force, and hence the amplitude of theresponse mode motion is directly proportional to the applied rotationrate. Other higher-order cos nθ mode pairs may also be used in similarfashion.

In operation, the carrier mode is driven at the resonance maximum and istypically maintained at a constant amplitude. The Coriolis forcesgenerated as a result of rotation will be at the carrier resonancefrequency. The response mode frequency is typically matched to that ofthe carrier and thus the motion arising as a result of these forces isamplified by the Q (quality factor) of the structure, giving enhancedsensitivity. This response mode motion may be nulled using a forcefeedback loop with the nulling force then being directly proportional tothe applied rate. This mode of operation removes the Q dependence fromthe rate output and gives improved scalefactor performance. The motionof the ring is thus maintained at a fixed angular orientation at alltimes.

Planar ring structures are also suitable for use in single-axis attitudesensors using in-plane cos nθ mode pairs, such as described in relationto a cylindrical element in U.S. Pat. No. 5,218,867. In this mode ofoperation, the vibration energy is free to transfer between the in-planemode pairs as the device is rotated, with no force feedback beingapplied. If the mode frequencies are accurately matched, this will beequivalent to the mode rotating around the ring as the structure isrotated. The mode pattern orientation is not inertially stable but tendsto lag behind the rotation of the ring structure. The ratio of thepattern angle rotation to the applied rotation angle is given by aninertial coupling constant, K, which is dependent upon the resonatorstructure and the mode order, n.

When operating in this mode, the same drive and pick-off configurationsmay be employed as for conventional closed-loop rate gyro operation. Thetechniques for detecting the mode orientation on the ring and formaintaining the amplitude of motion are, however, significantlydifferent. A radial drive signal is applied to sustain the vibrationamplitude at one or more of the radial anti-nodes. As the mode patternrotates around the ring, the effective drive position is required totrack the radial anti-node around the ring. The pick-offs must similarlyhave the capability of resolving the actual radial motion of the ring atboth the radial anti-node and node. The radial anti-node signal is usedto maintain the drive frequency at the resonance maximum and tonormalise the vibration amplitude. The radial node signal is required totrack the mode position accurately.

Ring structures are also capable of providing rate sensitivity aroundmultiple axes, as described in UK Patent Application Nos. 2318184A and2335273A. When driven in a cos nθ in-plane carrier mode, rotations aboutaxes in the plane of the ring will also give rise to Coriolis forces.These forces will be along the axis normal to the plane of the ring(z-axis). For rotation around the y-axis Ω_(y), where the y-axis istaken to be along θ=0°, these Coriolis forces, F_(z)(θ), will have anangular distribution given by:

F _(z)(θ)=F _(n+1)Ω_(y) sin(n+1)θ+F _(n−1)Ω_(y) sin(n−1)θ

where θ is the angular position around the ring with respect to a fixedreference position, n is the carrier mode order and the parameters F⁻¹and F_(n+1) are constants which depend on the precise geometry of thering, the material from which the ring is made, and the value of n.Similarly, for rotation about the x-axis, Ω_(x), the Coriolis forceswill have an angular distribution given by:

F _(z)(θ)=F _(n−1)Ω_(x) cos(n+1)θ−F_(n−1)Ω_(x) cos(n−1)θ

These forces thus have components that are capable of directly excitingeither the sin(n−1)θ and cos(n+1)θ or the sin(n−1)θ and cos(n−1)θout-of-plane mode pairs. The rin dimensions may be set such that theresonant frequency of one of the mode pairs exactly matches that of thein-plane carrier mode. In this way, the amplitude of the out-of-planeresponse motion will be amplified by the Q of the structure as for thein-plane response.

Using such designs, a single device can provide all the functionalityrequired for navigation applications where previously two or threesingle-axis devices would be needed, one device being dedicated to eachaxis. Multi-axis devices have the advantage that the mutual alignment ofthe sensing axes is set during the resonator fabrication process, andyet single-frequency operation for all axes means that the electronicsneed not be significantly more complex than in a single-axis device. Forapplications requiring rate sensitivity around multiple axes, such amulti-axis device may provide a significant reduction in both cost andsize.

Between them, UK Patent Application Nos. 2318184A and 2335273A describevarious modal combinations that may be employed to implement both two-and three-axis rate gyroscopes. The locations of the drive and pick-offtransducer elements appropriate for each combination are also showntherein.

The disclosures of U.S. Pat. No. 5,218,867 and UK Patent ApplicationNos. 2318184A and 2335273A are incorporated herein by reference.

Certain gyroscope applications may require measurement of the spatialorientation of a body that is subject to high rates of rotation aboutone particular axis. In aircraft navigation, for example, the roll axisof the aircraft may be subject to higher rotation rates than the pitchand yaw axes. In order to compute the orientation in the pitch and yawaxes in such applications, it is essential that the orientation in theroll axis is known to a high degree of accuracy.

Consequently, for axes experiencing high rotation rates, there is aconsiderable performance advantage in operating in “whole angle” mode toprevent the accumulation of a heading error due to scalefactor error. Byway of illustration, a 1% scalefactor error will result in a 3.6°heading error for each revolution. This problem of cumulative error isparticularly acute when sensing the motion of a wheel or axle, in whichone axis will obviously experience vastly higher rotation rates than theother two axes.

There is therefore a requirement for a device that combines theadvantages of multi-axis operation whilst providing for accuratemeasurement of orientation around a single axis that may be subject tosustained high rates of rotation.

SUMMARY OF THE INVENTION

The present invention results from the insight that it is possible tooperate the z-axis response of a multi-axis gyroscope in “whole angle”or “gyroscope” mode whilst retaining the x- and y-axis responses in rategyro mode. Accordingly, the invention may be expressed broadly as athree-axis gyroscopic sensing device adapted for operation as a rategyroscope about two axes and as a whole angle gyroscope about the thirdaxis.

The invention therefore resides in a vibrating structure gyroscopecomprising a resonant body, drive transducer means for driving resonantmotion of the body, pick-off means for producing signals representive ofthe resonant motion, and signal processing means for extracting z-axisorientation information and x- and y-axis rate information from thesignals, such that the gyroscope operates as a whole angle gyroscope forrotations about the z-axis and as a rate angle gyroscope for rotationsabout the x-axis and y axis.

More specifically, the signal processing means extracts z-axis carriermode orientation information from the signals and normalises thisinformation to give information on the angular orientation about thez-axis, as well as extracting x- and y-axis rate information from thesignals.

In such a gyroscope the resonant body is typically a planar ringstructure and the resonant motion takes place in a vibration modepattern in the plane of the ring whose orientation angle with respect tothe body varies proportionately with the orientation of the body aboutits z-axis. This vibration mode pattern couples energy into anout-of-plane response mode motion in accordance with rotation of thebody about the x- or y-axis. In this case, the signal processing meansadvantageously resolves the out-of-plane response mode motion withreference to a z-axis orientation signal representative of theorientation about the z-axis to extract the x- and y-axis rateinformation.

The pick-off means suitably comprises a first plurality of pick-offspositioned to sense resonant motion in the plane of the body and asecond plurality of pick-offs positioned to sense response mode motionout of the plane of the body. The pick-offs of the second pluralityshould be separated by 30 k°, where k is an odd integer.

The drive transducer means preferably comprises a plurality of drivetransducers driven via a drive resolver that takes input from the z-axiscarrier vibration mode orientation signal to give a resultant driveresolved along the orientation angle of the vibration mode pattern.

In preferred embodiments of the invention, the signal processing meansincludes rate integration means that takes input signals from the firstplurality of in-plane pick-offs via a pick-off resolver and outputs thez-axis orientation signal, and an x- y-axis resolver that takes as inputdrive signals applied to a plurality of out-of-plane drives, resolvesthose signals with reference to the z-axis carrier vibration modeorientation signal, and outputs the x- and y-axis rate information.

Advantageously, an anti-nodal signal from the pick-off resolver isapplied to a phase locked loop that adjusts the drive frequency of thedrive transducer means to track a resonance maximum. The anti-nodalsignal is preferably also applied to a gain control loop that adjuststhe drive level applied to the drive transducer means to maintain aconstant anti-nodal signal.

A nodal signal from the pick-off resolver may be applied to a rateintegration means that preferably comprises a phase detector to resolveany signal component that is in-phase with an anti-nodal signal. Therate integration means advantageously comprises a rate signal generatormeans such as a loop controller that takes the nodal signal and outputsa rate signal proportional to the rate of rotation of the vibration modepattern about the z-axis. The rate integration means can then furthercomprise an integrator that integrates the rate signal to output thez-axis carrier vibration mode orientation signal. This z-axis carriervibration mode orientation signal can be applied to a normalising meansthat applies the Bryan factor to that signal to give a direct measure ofthe angle through which the gyroscope body has rotated around thez-axis.

Conveniently, the pick-off means comprises an x-axis pick-off whoseoutput is applied to an x-axis rate loop and a y-axis pick-off whoseoutput is applied to a y-axis rate loop and the x- and y-axis rate loopsrespectively apply drive signals to x- and y-axis drive transducers tonull the signal at the respective pick-offs.

To minimise vibration pattern drift, it is advantageous to employ aquadrature nulling loop. This loop preferably applies a drive signal tothe drive transducer means along a nodal axis to maintain the input tothe loop at zero.

BRIEF DESCRIPTION OF THE DRAWINGS

For a better understanding of the present invention and to show how itmay be carried into effect, reference will now be made, by way ofexample, to the remaining drawings in which:

FIG. 1a shows diagrammatically a degenerate cos 2θ vibration mode in asymmetric resonator or vibrating structure acting as a carrier mode in aconventional manner,

FIG. 1b is a diagrammatic illustration of a degenerate sin 2θ vibrationmode at 45° to that FIG. 1a, acting as a response mode in a conventionalmanner.

FIG. 2a is a three-dimensional representation showing the angulardistribution of radial displacement for a cos 2(θ+α) in-plane carriermode where α=0°;

FIG. 2b corresponds to FIG. 2a but shows the cos 3θ vibration modepattern of z-axis displacement excited by rotation around the x-axis;

FIG. 2c corresponds to FIGS. 2a and 2 b but shows the sin 3θ vibrationmode pattern of z-axis displacement excited by rotation around they-axis;

FIGS. 3a, 3 b and 3 c correspond respectively to FIGS. 2a, 2 b and 2 cbut show the equivalent responses where α=22.5°;

FIG. 4 is a block diagram of a preferred embodiment of the inventionshowing components that implement z-axis angle sensing; and

FIG. 5 is a block diagram corresponding to FIG. 4 but showing additionalcomponents that implement x- and y-axis rate sensing.

DETAILED DESCRIPTION OF EMBODIMENTS

To recap, the present invention contemplates a multi-axis sensing devicethat operates as a rate gyroscope about two axes, x and y, and as a“whole angle” gyroscope about the third axis, z. With the z-axisgyroscope response implemented in this mode, the carrier mode for the x-and y-axis rate responses is no longer spatially fixed on the ring. Arotation applied around the z-axis will therefore result in the in-planecarrier mode angular position rotating around the ring.

The carrier mode shape may be defined with respect to a fixed angularreference direction. θ=0°, which is taken to be along a diameter passingthrough the ring centre. The radial displacement of the ring will have acos n(θ+α) angular distribution, where α is the mode angular orientationwith respect to the reference direction. The x and y rate response axesmay also be defined with respect to the fixed gyroscope body referenceaxis, the y-axis lying along θ=0° and the x-axis lying along θ=90°.

In order to derive the Coriolis force components generated as a resultof rotation around the x- and y-axes, it is necessary to consider theangular distribution of the radial and tangential velocity components ofthe carrier mode, for any given value of α. From this, the velocitycomponents in the x and y directions can be calculated and hence theCoriolis force distributions arising from rotations around the x- andy-axes.

For a rotation around the x-axis, Ω_(x), the out-of-plane Coriolis forcedistribution. F_(z)(θ), will be given by:

 F _(z)(θ)=F _(n−1)Ω_(x) cos{nα+(n+1)θ}+F _(n−1)Ω_(x) cos{nα+(n−1)θ}

where as before, θ is the angular position around the ring with respectto the fixed reference position, n is the carrier mode order and theparameters F_(n+1) and F_(n−1) are constants that depend on the precisegeometry of the ring, the material from which the ring is made, and thevalue of n. Similarly, for rotation around the y-axis, Ω_(y), theCoriolis force distribution will be given by:

F _(z)(θ)=F _(n+1)Ω_(y) sin{nα+(n+1)θ}+F _(n−1)Ω_(y) sin{nα+(n−1)θ}

It will be apparent that these expressions are similar to those obtainedfor a fixed carrier mode position as previously discussed, except forthe additional nα terms. Rotations around the body-fixed x and y axeswill therefore still result in the generation of Coriolis forcecomponents that can couple directly into cos(n±1)θ or the sin(n±1)θout-of-plane mode pairs. However, these force components will also bedisplaced by an angle nα on the ring.

These effects may be illustrated, by way of example, for a cos 2(θ+α)in-plane carrier mode coupling into cos(3θ+2α) and sin(3θ+2α)out-of-plane response modes. FIG. 2a shows a three-dimensionalrepresentation of the radial displacement angular distribution for a cos2(θ+α) in-plane carrier mode for α=0°. The broken line shows theundisplaced position of the ring with the solid lines showing theextremes of motion during a single vibration cycle.

A rotation applied around the x-axis will generate Coriolis forcecomponents which will excite a vibration mode pattern with z-axisdisplacements as shown in FIG. 2b. Again, the solid lines show theextremes of out-of-plane displacement from the stationary ring (dashedline) during the vibration cycle. Similarly, rotation applied around they-axis will excite a vibration mode pattern as shown in FIG. 2c.

FIG. 3 shows the equivalent responses where α=22.5°. FIG. 3a shows thein-plane radial carrier mode displacement and FIGS. 3b and 3 c show theout-of-plane response motion resulting from rotation applied around thex- and y-axes respectively. Similar plots may be generated for othermodal combinations.

Using this combination of modes, it is necessary to resolve thecos(3θ+2α) out-of-plane response mode motion in order to measurerotation around the x-axis of the gyro body. Similarly, to measurerotation around the y-axis it is necessary to resolve the sin(3θ+2α)out-of-plane response mode motion. The amplitude of motion of thesemodes is conveniently measured at one or more of the vibrationanti-nodes. As these anti-nodal points are no longer fixed on the ring,the x- and y-axis responses cannot be detected directly by fixedout-of-plane (z-axis) pick-off elements. The relevant motions can,however, be resolved in the required angular directions by combining theoutput of two or more appropriately located fixed pick-off elements.Where these response modes are operated in a force feedback mode, theappropriate drive forces may similarly be applied at the requiredresolved angular locations using two fixed drive transducers.

The control circuit for the in-plane rate integrating vibration modecontrol is shown in FIG. 4. The 0° direction is indicated by the solidarrow 9. Two drive elements 10 and 11 are located at 0° and 45° and twopick-off elements 12 and 13 are located at 180° and 225°.

For a known value of α, the sine/cos pick-off resolver 14 processes thesignals from pick-off elements 12 and 13 and outputs one signal resolvedalong the anti-nodal position and another signal resolved along thenodal position.

The anti-nodal signal is applied to a phase locked loop 15 which adjuststhe drive frequency to track the resonance maximum. This signal is alsoapplied to a gain control loop 16 which adjusts the drive level tomaintain a constant signal and thus to stabilise the vibrationamplitude. The drive signal V₀ is applied to the drive resolver element17 which sets the drive levels on drive transducers 10 (V₀cos 2α) and 11(V₀sin 2α) to give a resultant drive resolved along α.

The nodal pick-off signal is applied to a phase detector 18 thatresolves the signal component which is in-phase with the anti-nodalsignal. This signal is then applied to the RIG loop controller 19 togive a signal proportional to the rate of rotation of the vibration modepattern. This output is applied to an integrator 20 to give a signaldirectly proportional to the vibration mode pattern orientation angle α.This value is applied to the sine/cos pick-off resolver 14 such that anull value is maintained at the phase detector 18 output. Theorientation angle α is also applied to the sine/cos drive resolver 17 inorder to maintain the resolved drive along the anti-nodal axis.

For a non-perfect resonator structure, a small difference in the sin 2θand cos 2θ mode frequencies will give rise to a significant amount ofquadrature motion at the radial nodal points. This is known to give riseto undesirable vibration pattern drift but may be eliminated by nullingthe quadrature motion of the resonator by means of a quadrature nullingloop 21 as shown in FIG. 4. This resolves the component of the nodalsignal that is in quadrature to the anti-nodal signal and applies adrive signal along a nodal axis such that the input to the quadraturenulling loop 21 is zero at all times.

The α value derived from the integrator 20, when normalised at 22 by theBryan factor, gives a direct measure of the angle through which thegyroscope body has rotated around the z-axis.

The implementation of the x- and y-axis rate sensing is shownschematically in FIG. 5. For the out-of-plane rate response modes it isconvenient to use two pick-off elements 23 and 24 located at 0° and 90°with respect to the fixed reference axis although any two pick-offelements separated by 30 k° (where k is an odd integer) will besuitable. These pick-off elements are positioned appropriately aboveand/or below the ring rim to detect out-of-plane motion. Similarly, itis convenient to use two drive transducer elements 25 and 26 located at180° and 270° to control the out-of-plane motion of the ring.

FIG. 5 shows the electronic control circuitry for the z-axis rateintegrating mode discussed above in combination with x- and y-axis rategyro operation. The primary loops 27 include both the phase locked 15and gain control 16 loops illustrated in FIG. 4 for the in-plane carriermode. Similarly, the rate integration loop 28 includes the phasedetector 18, RIG loop controller 19 and integrator 20 of FIG. 4.

The output of x-axis pick-off 23 is applied to the x-axis rate loop 29and a drive is applied to the x-axis drive element 25 in order to nullthe signal at the pick-off 23. Similarly, the output of y-axis pick-off24 is applied to the y-axis rate loop 30 and a drive is applied to they-axis drive element 26 in order to null the signal at the pick-off 24.

Where the in-plane and out-of-plane modes are all precisely matched infrequency, the out-of-plane response mode motion will be in phase withthe in-plane motion but where any small frequency split is present,quadrature motion will be detected. Additional drive signals may beapplied to the x- and y-axis drive elements 25 and 26 to null thisquadrature motion in order to maintain a true null at the pick-offelements 23 and 24.

While the x- and y-axis drive and pick-off transducer elements 23, 24,25, 26 are aligned along the input rotation axes, the responses to rateinputs about these axes are dependent upon the orientation of thecarrier mode pattern, α. The applied rates must be resolved from theseresponses using the in-plane carrier mode angular location α. The drivesignals from the x- and y-axis loops 29, 30 are applied to the sine/cosx-y axis resolver 31 and the in-phase drive levels are resolved along α(cos(3θ+2α) response) and α+30° (sin(3θ+2α) response) to obtain the x-and y-axis rate signals.

Many variations are possible within the inventive concept. For example,additional drive and pick-off elements may be located at additionalangular locations matched to the modal symmetry of the vibrating elementwithout changing the basic functionality of the device. More generally,the control scheme of the invention may be used with any of the in-planecarrier and out-of-plane response modal combinations described in UKPatent Application Nos. 2318184A and 2335273A.

Those skilled in the art will also know that that the resonator elementcould be made from various materials, such as electro-formed ormicro-machined metal, quartz, polysilicon or bulk silicon. The choice ofmaterial will often be determined by the fabrication method and viceversa. It will also be apparent that the drive means and/or the pick-offmeans can operate using various principles, notably electrostatics,electromagnetics, piezoelectricity or optics.

What is claimed is:
 1. A vibrating structure gyroscope comprising: aresonant body, drive transducer means for driving resonant motion of thebody, pick-off means for producing signals representative of theresonant motion, and signal processing means for extracting z-axiscarrier vibration mode orientation signal and for normalising saidsignal to give information on angular orientation about the z-axis andfor extracting x- and y-axis rate information from the signals, whereinthe gyroscope operates as a whole angle gyroscope for rotations aboutthe z-axis and as a rate angle gyroscope for rotations about the x-axisand the y-axis.
 2. The gyroscope of claim 1, wherein the resonant bodyis a planar ring structure and the resonant motion takes place in avibration mode pattern in the plane of the ring structure whoseorientation angle with respect to the body varies proportionately withthe orientation of the body about the z-axis and couples energy into anout-of-plane response mode motion in accordance with rotation of thebody about the x- or y-axis, and wherein the signal processing meansresolves the out-of-plane response mode motion with reference to az-axis orientation signal representative of orientation about the z-axisto extract the x- and y-axis rate information.
 3. The gyroscope of claim2, wherein the pick-off means comprises a first plurality of pick-offspositioned to sense resonant motion in the plane of the body and asecond plurality of pick-offs positioned to sense response mode motionout of the plane of the body.
 4. The gyroscope of claim 3, wherein thepick-offs of the second plurality are separated by 30k°, where k is anodd integer.
 5. The gyroscope of claim 2, wherein the drive transducermeans comprises a plurality of in-plane drive transducers driven via adrive resolver that takes input from the z-axis orientation signal togive a resultant drive resolved along the orientation angle of thevibration mode pattern.
 6. The gyroscope of claim 3, wherein the signalprocessing means includes rate integration means that takes inputsignals from the first plurality of in-place pick-offs via a pick-offresolver and outputs the z-axis orientation signal, and an x- y-axisresolver that takes input drive signals applied to a plurality ofout-of-plane drive transducers, resolves said drive signals withreference to the z-axis orientation signal, and outputs the x- andy-axis rate information.
 7. The gyroscope of claim 6, wherein ananti-nodal signal from the pick-off resolver is applied to a phaselocked loop that adjusts the drive frequency of the drive transducermeans to a track a resonance maximum.
 8. The gyroscope of claim 7,wherein the anti-nodal signal is applied to a gain control loop thatadjusts the drive level applied to the drive transducer means tomaintain a constant anti-nodal signal.
 9. The gyroscope of claim 6,wherein a nodal signal from the pick-off resolver is applied to the rateintegration means.
 10. The gyroscope of claim 9, wherein the rateintegration means comprises a phase detector that resolves the signalcomponent which is in-phase with an anti-nodal signal.
 11. The gyroscopeof claim 9, wherein the rate integration means comprises a rate signalgenerator means that takes the nodal signal and outputs a rate signalproportional to the rate of rotation of the vibration mode pattern aboutthe z-axis.
 12. The gyroscope of claim 11, wherein the rate integrationmeans further comprises an integrator that integrates the rate signal tooutput the z-axis orientation signal.
 13. The gyroscope of claim 2,wherein the z-axis orientation signal is applied to a normalising meansthat applies the Bryan factor to the z-axis orientation signal to give adirect measure of the angle through which the body has rotated aroundthe z-axis.
 14. The gyroscope of claim 1, wherein the pick-off meanscomprises an x-axis pick-off whose output is applied to a y-axis rateloop, and the x- and y-axis pick-off whose output is applied to y-axisrate loop, and the x- and y-axis rate loops respectively apply drivesignals to x- and y-axis drive transducers to null respective pick-offsignals.
 15. The gyroscope of claim 1, wherein a quadrature nulling loopapplies a drive signal to the drive transducer means along a nodal axisto maintain the input to the quadrature nulling loop at zero.